Former Middlesbrough man Yakubu put Leicester 2-1 in front at half-time with close-range finishes on five minutes and in injury time with Marvin Emnes replying for Boro.
The on-loan Everton forward netted his third four minutes into the second half before Rhys Williams made it 3-2 with a 25-yard shot.
The Foxes looked like hanging on for the win with goalkeeper Chris Weale saving Julio Arca's penalty despite City playing out the last 13 minutes with 10 men after Jeffrey Bruma was sent off before McManus nodded home.
Despite not picking up all three points, Sven-Goran Eriksson's men moved to within four points of the top six whereas Boro, now unbeaten in four, remain nine points clear of the drop zone.
Source: PA
Source: PA